Ratio Problems with Totals and Differences - Worksheets, Questions and Revision

13 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

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KS3 · Ratio, Proportion and Rates of Change

KS3.M-R4 Ratio Problems with Totals and Differences

AQA KS3.M-R4 · Calculators not allowed · about 50 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Write the following ratios in their simplest form.
(a)Simplify the ratio 12 : 20(1)
(b)Simplify the ratio 18 : 27(1)
2
There are 24 pupils in a club. The ratio of boys to girls is 5 : 7. Work out the number of boys and the number of girls.
(a)How many boys are in the club?(1)
(b)How many girls are in the club?(1)
3
A recipe uses milk and water in the ratio 3 : 5. If you have 2 litres of milk, how much water do you need to keep the same ratio?
(single)Calculate the required volume of water in litres.(2)
4
The angles in a quadrilateral are in the ratio 2 : 3 : 4 : 5. Find the size of the largest angle.
(single)Work out the largest angle in degrees.(2)
5
Tom and Aisha share 84 pounds in the ratio 5 : 7. How much more does Aisha get than Tom?
(single)Find the difference between Aisha's share and Tom's share.(3)
6
A map scale shows 1 cm represents 6 km. On the map two towns are placed so the map distance between them is divided in the ratio 2 : 3 and the total map distance is 15 cm. What is the actual distance in km between the two towns?
(single)Calculate the actual distance in kilometres.(2)
7
Three numbers are in the ratio 1 : 4 : 5. The difference between the largest and the smallest is 36. Find the three numbers.
(single)Calculate the three numbers.(2)
8
A and B share a prize in the ratio 3 : 5. The difference between their amounts is 40 pounds. Work out A's share and B's share.
(single)Find A's share and B's share in pounds.(3)
9
A school has a ratio of teachers to teaching assistants of 7 : 2. If there are 81 staff members in total, how many teachers and how many teaching assistants are there?
(single)Find the number of teachers and the number of teaching assistants.(3)
10
A mixture contains sugar and water in the ratio 2 : 9. After adding 3 kg of sugar, the ratio becomes 5 : 9. How much sugar was in the mixture to start with?
(single)Find the initial mass of sugar in kilograms.(4)
11
Two numbers are in the ratio 7 : 11. Their total is 162. Find the two numbers.
(single)Calculate the two numbers.(4)
12
A class mixes red and blue paint in the ratio 4 : 7 to make purple. They need 33 litres of purple paint. How many litres of blue paint must they use? If they decide instead to add 2 litres more red paint but keep the blue the same, what will the new ratio of red to blue be?
(a)How many litres of blue paint are used?(3)
(b)If 2 litres more red are added but blue remains the same, what is the new ratio of red to blue? Give the ratio in its simplest whole-number form.(3)
13
Stretch question. A, B and C share an inheritance in the ratio 4 : 6 : 9. C then gives 70 to A and 10 to B. Now the three have equal amounts. Work out the original total inheritance.
(single)Find the original total inheritance in pounds.(5)
Mark scheme · KS3.M-R4 Ratio Problems with Totals and Differences

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13